An IWOA-based total segment alignment multi-objective trajectory optimization method

Abstract

The application provides a total section alignment multi-objective trajectory optimization method based on IWOA, which comprises the following steps: 1, determining a ship total section trajectory planning mode; 2, obtaining dynamic trajectory parameters required to be followed by a posture adjustment trolley in different directions; 3, realizing multi-objective trajectory optimization of the total section and the posture adjustment trolley; 4, planning total section posture adjustment, solving optimal time in a constraint range, and solving a posture adjustment trolley motion trajectory; 5, establishing a posture adjustment trolley total section alignment model; and 6, verifying the feasibility of total section trajectory multi-objective optimization and the accuracy of total section alignment trajectory planning. The beneficial effects are as follows: through automatic alignment system construction, high-precision measurement system construction, coordinate transformation model, point set matching algorithm, intelligent optimization algorithm, trajectory planning algorithm and ship total section automatic alignment trajectory planning system, efficient and accurate automatic alignment of the ship total section is realized.

Description

Technical Field

[0001] This invention relates to a multi-objective trajectory optimization method for overall segment alignment based on IWOA, belonging to the field of shipbuilding technology. Background Technology

[0002] With sustained global economic growth and robust demand in the shipping industry, and driven by the independent research and development of new technologies by leading shipbuilding nations, shipbuilding technology has achieved a tremendous leap forward. The world's leading shipbuilding nations are forming a rapid response model for shipbuilding. Currently, shipbuilding generally adopts the modular shipbuilding method. This method uses ship sections as manufacturing units, employing cranes to move the sections assembled in location A to location B for assembly into a complete ship. This allows for full utilization of assembly facilities, forming a parallel, batch production model for shipbuilding in different locations. This model reduces the amount of welding and assembly work on the slipway, helping to shorten the shipbuilding cycle.

[0003] In this model, the assembly of ship sections is a key process in shipbuilding, directly impacting the overall efficiency and precision of the vessel. Currently, the development of the shipbuilding method using the main assembly section method in China has not achieved the expected results. A major challenge stems from the fact that the alignment process relies heavily on manual visual inspection and adjustments, leading to low efficiency, poor precision, and difficulty in achieving efficient and accurate assembly in one go. Traditional methods for aligning main sections require first hoisting a fixed section onto the slipway, followed by hoisting subsequent sections. Then, measuring instruments are used to measure the positional relationship between the sections, and subsequent sections undergo two positioning checks to ensure accuracy. Under traditional methods, the alignment process requires multiple measurements and positioning checks to ensure the positional relationship between the sections, making the overall alignment process cumbersome, inefficient, and inaccurate.

[0004] Currently, domestic shipyards require long-term use of core production equipment such as cranes for the assembly of ship sections, easily creating a bottleneck in the shipbuilding process and significantly hindering efficiency. Furthermore, when cranes lift sections for alignment, factors such as the difficulty in detecting rope deformation and variable force directions often lead to significant alignment errors. Simultaneously, as the size and weight of hull sections increase, traditional visual, marking, and manual methods are becoming increasingly inadequate to guarantee the efficiency and accuracy of alignment. This not only introduces enormous stress into the welding areas of the sections but also negatively impacts the ship's construction quality and increases safety risks during operation. In modern section-based shipbuilding, achieving efficient and precise section alignment has become a crucial step in the ship assembly process.

[0005] Currently, the rapid development of automated alignment technology has led to the automation and digitalization of the assembly process, significantly reducing manpower, shortening alignment time, and improving alignment accuracy. This technology is particularly evident in the assembly processes of aircraft and aerospace equipment, while research and application in the field of ship assembly alignment are still in their early stages.

[0006] Although my country's shipbuilding industry ranks among the top in global output, there is still significant room for improvement in quality. In the crucial area of ​​assembly section alignment technology, my country lags behind world-leading levels, and the low efficiency and poor precision in assembly section alignment severely hinder the vigorous development of my country's shipbuilding industry. Therefore, introducing advanced technologies such as next-generation information technology and artificial intelligence into the shipbuilding industry to promote efficient and precise automated alignment of ship assemblies is an inevitable choice for my country to develop automated, intelligent, and digital shipbuilding and accelerate its construction into a shipbuilding powerhouse. Summary of the Invention

[0007] Purpose of the invention: To address the shortcomings of existing technologies, this invention provides a multi-target trajectory optimization method for ship section alignment based on IWOA. It achieves efficient and accurate automated alignment of ship sections through the construction of an automated alignment system, a high-precision measurement system, a coordinate transformation model, a point set matching algorithm, an intelligent optimization algorithm, a trajectory planning algorithm, and an automatic alignment trajectory planning system for ship sections.

[0008] Technical solution: A multi-target trajectory optimization method based on IWOA (Integrated Wound Alignment), comprising the following steps:

[0009] Step 1: Select the alignment method based on the completed attitude adjustment trolley position and attitude calculation results, and adjust the position and attitude of the ship section through the coordinated operation of the attitude adjustment trolley; and determine the trajectory planning method of the ship section according to the given task requirements.

[0010] Step 2: View the main section and its supporting attitude adjustment trolley as an automatic alignment parallel system integrating six degrees of freedom. The main section serves as the mobile platform, while multiple attitude adjustment trolleys constitute the power support of the system. By performing inverse kinematics analysis on the system, the dynamic trajectory parameters that the attitude adjustment trolleys need to follow in different directions are obtained.

[0011] Step 3: Based on the determined overall alignment method and trajectory planning method, and combined with the speed and acceleration constraints of the attitude adjustment vehicle, establish a multi-objective function of time-energy consumption-impact degree, and further solve the multi-objective optimization model through the improved whale algorithm to achieve multi-objective trajectory optimization of the overall segment and the attitude adjustment vehicle.

[0012] Step 4: Simulate and analyze the multi-objective optimization process. Following the posture calculation results of the attitude adjustment vehicle in Step 1, and combining the speed and acceleration constraints of the attitude adjustment vehicle, plan the attitude adjustment of the whole segment. During the rotation and translation of the whole segment, use the bisection method to solve for the optimal time within the constraint range. Based on the above multi-objective function, use the improved whale algorithm to solve the objective function, thereby calculating the time of the rotation and translation process of the whole segment. Through time parameters, seventh-order polynomial trajectory planning method, and speed and acceleration constraints of the attitude adjustment vehicle, solve for the motion trajectory of the attitude adjustment vehicle.

[0013] Step 5: While ensuring that the basic motion mode and motion constraints of the attitude adjustment vehicle are consistent, simplify the design model of the attitude adjustment vehicle and use ADAMS software to establish the overall alignment model of the attitude adjustment vehicle without an internal transmission system.

[0014] Boolean constraints and kinematic pair constraints are added to the established model. Boolean constraints combine multiple parts of the orientation adjustment vehicle into fewer parts, facilitating kinematic simulation. Simultaneously, kinematic pair constraints define the motion directions of the parts within the orientation adjustment vehicle. Then, a kinematic simulation of the overall segment alignment is performed, and the accuracy of the trajectory planning is assessed based on the simulation results.

[0015] Step 6: Conduct multi-objective optimization experiments and overall alignment experiments for the entire segment to verify the feasibility of multi-objective optimization of the segment trajectory and the accuracy of the overall alignment trajectory planning.

[0016] Step 1 specifically involves:

[0017] A two-step alignment method is adopted as the overall segment posture adjustment alignment method. The two-step alignment method is as follows:

[0018] First, the roll, pitch, and yaw angles of the ship section are adjusted to achieve angular alignment. Then, fine position adjustments are made in the three main axis directions X, Y, and Z to complete the entire alignment operation.

[0019] The trajectory of the ship's total section is planned using a seventh-order polynomial. The expression for the seventh-order polynomial planning is as follows:

[0020]

[0021] Let the initial time be t0=0 and the final time be t f Its constraints are:

[0022]

[0023] Substituting the constraints into the above equation, the values ​​of each parameter can be solved:

[0024]

[0025] make The trajectory of α can be obtained:

[0026]

[0027] Similarly, the trajectories of the total segments x, y, z, β, and γ can be obtained:

[0028]

[0029] Step 2 specifically involves:

[0030] Step 2.1: Measure the position of the center of the rotating ball head of the attitude adjustment trolley, and convert the measurement data to the coordinate system of the moving section. The positions of the center of the rotating ball head of each trolley in the coordinate system of the moving section are as follows: , where n represents the number of attitude adjustment vehicles;

[0031] During the rotation of the main segment, the inverse kinematics of the attitude adjustment trolley is solved by the rotation matrix; during the translation of the main segment, only the simultaneous movement of four attitude adjustment trolleys is needed to achieve the translation of the main segment, so the trajectory of each trolley is consistent with the above-mentioned translation trajectory of the main segment.

[0032] The rotational adjustment of the main section takes time t1, and the translational adjustment of the main section takes time t2. Therefore, during the overall adjustment process of the ship's moving main section, the relative displacement of the adjustment trolley in the three degrees of freedom is:

[0033]

[0034] In the formula, R(t) is:

[0035]

[0036]

[0037]

[0038]

[0039] And in the formula, Taking the derivative of the above equation as a function of angle and time, we can obtain the expression for the velocity motion of each degree of freedom during the adjustment process of the overall segment rotation:

[0040]

[0041] Differentiating the above equation, we obtain the expression for the acceleration motion of each degree of freedom of the entire segment during the attitude adjustment process:

[0042]

[0043] Differentiating the above equation, we obtain the expression for the acceleration motion of each degree of freedom of the entire segment during the attitude adjustment process:

[0044]

[0045] Step 2 specifically involves:

[0046] Step 2.2: Constrain the velocity and acceleration of each attitude adjustment trolley. The constraint conditions are as follows:

[0047]

[0048] During the rotation of the entire section, the maximum velocity of each degree of freedom of the attitude adjustment trolley is limited to 10 mm / s, and the acceleration is limited to 2 mm. 2 / s; During the overall translation process, the maximum velocity of each degree of freedom of the attitude adjustment trolley is limited to 30mm / s, and the acceleration is limited to 2mm. 2 / s.

[0049] Step 3 specifically involves:

[0050] Step 3.1: Establish the objective function for trajectory optimization.

[0051] To address the issues of high energy consumption and significant impact during attitude adjustment in large ship section automatic alignment systems, multi-objective programming is implemented for each trolley during the overall attitude adjustment process of the section, and the objective function is defined as follows:

[0052]

[0053] In the formula, st is the total number of pose adjustment steps, st=2; t i This represents the time taken in step i; T is the running time of the attitude adjustment trolley, and N represents the number of trolleys, N=4; , f1 represents the total acceleration and total jerk of the nth attitude adjustment vehicle in the three degrees of freedom during step i; f2 represents the motion time of the entire attitude adjustment process; f3 represents the energy consumption index of all attitude adjustment vehicles during the attitude adjustment process; f4 represents the joint impact index of all attitude adjustment vehicles.

[0054] Step 3.2: Solving the integral based on Simpson's method

[0055] Solving Simpson's integrals by dividing the integration interval [a, b] into many intervals, i.e., the composite Simpson's integral method, involves dividing the integration interval [a, b] into 2n equal-width subintervals [x, b, ..., x]. k x k +1], the length of each interval is Let 2n be the number of subintervals, and n be a positive integer. Then the corresponding composite Simpson integral formula is as follows:

[0056]

[0057] In the formula, a=0; b=t1, representing the completion time of the first stage of the overall segment;

[0058] The error formula is:

[0059]

[0060] In the formula, f (4) It is the maximum value of the fourth derivative of f(x) in the interval [a, b], where .

[0061] Step 3 specifically involves:

[0062] Step 3.3: Solve the multi-objective optimization model using the improved whale algorithm to achieve multi-objective trajectory optimization for the total segment and the attitude adjustment vehicle. Specifically:

[0063] An improved whale optimization algorithm was obtained by improving the population initialization, weights, convergence factor, and search capability in the whale optimization algorithm.

[0064] The initialization of the population in the improved whale optimization algorithm is optimized by using Hammersley low-discrepancy sequences to improve the initial distribution of the population and promote its uniformity. The formula for using the Hammersley sequences to generate the initial population is shown below:

[0065]

[0066] In the formula: x i The initial position of the individual; X lb This represents the lower limit of an individual variable; X ub The upper limit of the individual variable; H is a random number in the [0, 1] range generated by Hammersley;

[0067] The weights of the population in the whale optimization algorithm are improved by introducing the weight concept from the particle swarm optimization algorithm into the whale algorithm. In order to address the problem that the weights are generally linear functions and have poor convergence, an adaptive weight strategy is proposed.

[0068]

[0069] After adding weights, the position update formula for the whale algorithm is:

[0070]

[0071]

[0072]

[0073] The convergence factor of the population in the improved whale optimization algorithm is changed from a non-linear decrease to a non-linear decrease. The update formula for the non-linear convergence factor is:

[0074]

[0075] To improve the population search capability of the whale optimization algorithm, in IWOA, c is replaced with the isotropic Lévy step size, and the process is as follows:

[0076]

[0077]

[0078]

[0079] In the formula, Levy is the step size extracted from the Levy distribution, and Γ(λ) is the standard gamma function. U and V follow normal distributions with a mean of zero, and σ 2 u and σ 2 v Let Variance be the variance.

[0080] Step 3 specifically involves:

[0081] Step 3.4: Solving the objective function based on IWOA

[0082] Before using the IWOA algorithm to solve the time-energy-impact function, the objective function is normalized to eliminate dimensions. The normalization formula is as follows:

[0083]

[0084] In the formula: f inew f is the new dimensionless function after normalization of the i-th objective function; i (x) min f is the minimum function value of the i-th objective function within the range; i (x) max Let be the maximum function value of the i-th objective function within the range;

[0085] To better determine the weight of each objective in the optimization process, the normalized objective function is weighted, and the constructed normalized weighted objective function is as follows:

[0086]

[0087] In the formula, , , The weighting coefficients define the importance of each objective in the alignment of the ship sections. Different projects have different focuses and therefore assign different weights. This study aims to find the most balanced values ​​and assigns them according to an equal weighting method. ;

[0088] By adding an external penalty factor to the objective function, the fitness of parameters outside the constraints is increased. When searching for the minimum of the objective function, the process of updating the population optimum is skipped. The objective function after adding the penalty factor is:

[0089]

[0090] In the formula, f(x) represents an unconstrained initial function; K is the penalty coefficient, which is set to K=1000 in this study; Let g(x) be the maximum number of iterations; g(x) be the constraint condition. When the constraint condition is met, g(x) = 0; when the constraint condition is not met, g(x) = 1. By solving the above objective function and finding the two time intervals that minimize F(x) within the constraint range, the obtained time intervals are the optimal solutions under the multi-objective equilibrium condition.

[0091] Step 4 specifically involves:

[0092] Under the above-mentioned speed and acceleration constraints, the attitude adjustment of the whole segment is planned. During the rotation and translation of the whole segment, the bisection method is used to solve for the optimal time within the constraints.

[0093] Using a seventh-order polynomial trajectory fitting method and applying the bisection method, the solution time is as follows:

[0094]

[0095] In the formula This refers to the total alignment time of the segment;

[0096] Considering practical engineering conditions, the movement speed and working stroke of the three-dimensional adjustable trolley must meet certain constraints:

[0097]

[0098] Combining the kinematic equations summarized above, by selecting an appropriate total segment alignment time for the above equation, we can obtain the motion trajectories of each three-dimensional adjustable vehicle in each direction that satisfy the constraints. Considering that in engineering practice we generally require the total segment alignment time to be as small as possible, we adopt the minimum total segment alignment time as the objective of motion trajectory planning. The mathematical model is as follows:

[0099] Target constraint

[0100]

[0101] The optimization problem described above is solved using the bisection method, with the specific steps as follows:

[0102] Step (1): Based on the initial pose, target pose, and maximum speed requirements of the three-dimensional adjustable trolley in each direction of the hull section, a preliminary range of the alignment time [t1, t2] is given, and t is obtained. f =t1,t f The equation of the motion trajectory of the total segment pose at time t2 is:

[0103]

[0104]

[0105] Step (2): Based on the trajectory equation and kinematic equation of the overall pose above, calculate t respectively. f =t1,t f At time t2, the maximum speed of each three-dimensional adjustable trolley in the x, y, and z directions;

[0106] It should be noted that directly calculating the motion speed of each 3D adjustable vehicle in each direction using analytical methods is extremely complex. A simpler approach is to discretize the total alignment time, with the discretization time interval being as small as possible. Generally, it can be taken to be the same as the sampling period of the actual control system, that is, to approximate the motion speed of the 3D adjustable vehicle in each direction changes linearly within one sampling period. Then, the motion speed of the 3D adjustable vehicle in each direction at each time point can be calculated, thereby obtaining the maximum motion speed of the 3D adjustable vehicle in each direction at the current total alignment time.

[0107] Step (3), if t f =t1,t f =t2 does not satisfy the constraint condition, which means that the values ​​of t1 and t2 are incorrect. At this time, we should go back to step (1) to reset the range of the total segment docking time.

[0108] Step (4), if t f =t1,t f =f2 does not satisfy the constraint condition, then the optimal total segment alignment time t opt =t1, calculation ends;

[0109] Step (5), if t f =t1 does not satisfy the constraint condition, while t f =t2 satisfies the constraint conditions, then let ;

[0110] Step (6), if t fIf t3 satisfies the constraint condition, then let t2 = t3; otherwise, let t1 = t3. Repeat step 5 until t2 - t1 ≤ δ. opt =t1 is the optimal total segment alignment time;

[0111] Step (7): Substitute someone to obtain t f =t opt Equation of the total segment docking trajectory at time:

[0112]

[0113] By combining the kinematic equations, the displacement, velocity, and acceleration of the ball center of each three-dimensional adjustable trolley process joint in the X, Y, and Z directions at each moment can be obtained. The data is then output and saved to complete the calculation.

[0114] Beneficial Effects: This invention addresses the problem of high cost and large error caused by traditional segment merging trajectory planning that only considers time optimization while neglecting energy consumption and impact, by conducting research on multi-objective trajectory optimization based on the Improved Whale Optimization Algorithm (IWOA). First, a segment alignment trajectory planning strategy based on a seventh-order polynomial is proposed. Second, a multi-objective trajectory optimization model is established with time, energy consumption, and impact as objectives, and the model is solved based on IWOA. Finally, trajectory planning simulation analysis is performed using MATLAB and ADAMS software, and experimental verification is conducted.

[0115] A seventh-order polynomial was used to optimize the impact during the step-by-step alignment of the main sections; the improved whale algorithm has a faster iteration speed and higher accuracy than other algorithms. Experimental results show that the multi-objective trajectory optimization based on IWOA achieves a balanced optimization of time, energy consumption, and impact during the alignment trajectory of the main sections; the final alignment error of the key measurement points of the main sections is within 2.5mm, which meets the alignment requirements for the closure of the main sections of the ship.

[0116] A multi-objective trajectory optimization based on IWOA (Integrated Wave Arithmetic) was implemented, considering time, energy consumption, and impact intensity. First, a multi-objective parameter model for time, energy consumption, and impact intensity was established. Second, based on constraints, the multi-objective function was simplified using normalization and weighting principles. Then, IWOA was used to solve the objective function, yielding a balanced trajectory for time, energy consumption, and impact intensity. Next, the alignment trajectory for the ship sections was validated using ADAMS. Simulation results show that the planned trajectory can effectively achieve precise alignment of the ship sections. Finally, an optimization experiment was conducted to verify the alignment trajectory. The experimental results show that although the optimized trajectory is slightly longer in time, it reduces energy consumption and impact intensity performance. Furthermore, the final alignment accuracy of the ship sections remains within 2.5 mm, meeting the alignment accuracy requirements in the ship section assembly process. Attached Figure Description

[0117] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0118] Figure 1 This is a flowchart of the multi-target trajectory optimization process of the present invention.

[0119] Figure 2 This invention generates individual distribution maps using the randomization method and Hammersley sequences.

[0120] Figure 3 This is a schematic diagram of the initial state during the overall segment alignment process of the present invention.

[0121] Figure 4 This is a schematic diagram of the rotation of the entire segment during the alignment process of the present invention.

[0122] Figure 5 This is a schematic diagram of the overall segment translation during the overall segment alignment process of the present invention.

[0123] Figure 6 This is a trajectory diagram of the key measurement points in this invention.

[0124] Figure 7 This is a diagram showing the Euclidean distance error of the key measurement points in this invention.

[0125] Figure 8 The diagram shows the sensor distribution of a single vehicle (left) and the sensor distribution of the overall alignment system (right) according to the present invention.

[0126] Figure 9 The chart shows a comparison of energy consumption indicators (left) and impact indicators (right) for this invention.

[0127] Figure 10 This is a diagram showing the completion of the automatic alignment of the entire segment in this invention.

[0128] Figure 11 The images show the XYZ direction error (left) and Euclidean distance error (right) of the key measurement points in this invention. Detailed Implementation

[0129] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0130] In the description of this invention, it should be understood that the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0131] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0132] A multi-target trajectory optimization method based on IWOA (Integrated Wound Alignment) includes the following steps:

[0133] Step 1: Select the alignment method based on the completed pose calculation results of the attitude adjustment trolley. In this invention, the pose calculation results are as follows: the original pose is rotated by 1.5°, 2°, and -1.15° around its own coordinate system in XYZ directions, and moved by 200mm, -1000mm, and -100mm along the XYZ direction to transform it into the target pose.

[0134] The position and attitude of the ship's hull sections are adjusted through the coordinated operation of the attitude adjustment trolley; and the trajectory planning method of the ship's hull sections is determined according to the given task requirements.

[0135] Step 2: View the main section and its supporting attitude adjustment trolley as an automatic alignment parallel system integrating six degrees of freedom. The main section serves as the mobile platform, while multiple attitude adjustment trolleys constitute the power support of the system. By performing inverse kinematics analysis on the system, the dynamic trajectory parameters that the attitude adjustment trolleys need to follow in different directions are obtained.

[0136] Step 3: Based on the determined overall alignment method and trajectory planning method, and combined with the speed and acceleration constraints of the attitude adjustment vehicle, establish a multi-objective function of time-energy consumption-impact degree, and further solve the multi-objective optimization model through the improved whale algorithm to achieve multi-objective trajectory optimization of the overall segment and the attitude adjustment vehicle.

[0137] Step 4: Simulate and analyze the multi-objective optimization process. Similarly, based on the posture calculation results of the attitude adjustment vehicle in Step 1, and combined with the speed and acceleration constraints of the attitude adjustment vehicle, plan the attitude adjustment of the whole segment. During the rotation and translation process of the whole segment, the bisection method is used to solve the optimal time within the constraint range.

[0138] Based on the above multi-objective function, the improved whale algorithm is used to solve the objective function, thereby calculating the total rotation and translation process time. The motion trajectory of the attitude adjustment vehicle is then solved by using time parameters, seventh-order polynomial trajectory planning method, and speed and acceleration constraints of the attitude adjustment vehicle.

[0139] Step 5: While ensuring that the basic motion mode and motion constraints of the attitude adjustment vehicle are consistent, simplify the design model of the attitude adjustment vehicle and use ADAMS software to establish the overall alignment model of the attitude adjustment vehicle without an internal transmission system.

[0140] Boolean constraints and kinematic pair constraints are added to the established model. Boolean constraints combine multiple parts of the orientation adjustment vehicle into fewer parts, facilitating kinematic simulation. Simultaneously, kinematic pair constraints define the motion directions of the parts within the orientation adjustment vehicle. Then, a kinematic simulation of the overall segment alignment is performed, and the accuracy of the trajectory planning is assessed based on the simulation results.

[0141] Step 6: Conduct multi-objective optimization experiments and overall alignment experiments for the entire segment to verify the feasibility of multi-objective optimization of the segment trajectory and the accuracy of the overall alignment trajectory planning.

[0142] Step 1 specifically involves:

[0143] During the automatic alignment of the hull sections, after the pose calculation is completed, the position and attitude of the hull sections are adjusted through the coordinated operation of the attitude adjustment trolley. There are three alignment methods for this process: four-stage alignment, one-step alignment, and two-step alignment.

[0144] In engineering practice, single-stage alignment often falls short of high-precision requirements. Furthermore, during overall segment alignment, the coordinates of key measurement points and the movement of the attitude adjustment trolley can introduce errors. Directly using a one-time alignment strategy may lead to conflicts between the segment to be aligned and the fixed part due to these errors. Therefore, a two-step alignment strategy has emerged. This method first adjusts the roll, pitch, and yaw angles of the overall segment to achieve angular alignment, and then performs fine-tuning of the position in the three principal axis directions (X, Y, and Z) to complete the entire alignment process. This paper selects the two-step attitude adjustment method as the overall segment attitude adjustment alignment method.

[0145] Trajectory planning primarily defines the changes in position, velocity, and acceleration of an object along its trajectory. Based on the object's current attitude and the kinematic principles of the system, it aims to design a suitable path that ensures the object moves according to predetermined kinematic characteristics to achieve the desired position and attitude. Simply put, the purpose of trajectory planning is to develop an ideal movement route that adheres to kinematic and geometric constraints based on given task requirements.

[0146] There are many methods for automatic alignment trajectory planning of ship hull sections, and polynomial fitting is generally used in engineering. This invention mainly analyzes three trajectory fitting techniques: cubic, quintic, and seventh-order polynomials, aiming to determine the most suitable trajectory planning strategy based on the specific alignment requirements of the ship hull sections. Let the initial pose of the moving section be: The target pose is The overall trajectory planning method is analyzed.

[0147] The trajectory of the ship's total section is planned using a seventh-order polynomial. The expression for the seventh-order polynomial planning is as follows:

[0148]

[0149] Let the initial time be t0=0 and the final time be t f Its constraints are:

[0150]

[0151] Substituting the constraints into the above equation, the values ​​of each parameter can be solved:

[0152]

[0153] make The trajectory of α can be obtained:

[0154]

[0155] Similarly, the trajectories of the total segments x, y, z, β, and γ can be obtained:

[0156]

[0157] The seventh-order polynomial fitting takes into account a more balanced force distribution at the contact point with the adjustment device, reducing the risk of deformation and damage to the main section. Therefore, using a seventh-order polynomial for trajectory design is particularly important to ensure the safety and stability of the automatic alignment process of the main section.

[0158] Step 2 specifically involves:

[0159] Although the ideal motion path of the main section has been determined, in practical operation, the dynamic parameters of the four attitude adjustment trolleys must be accurately calculated. Based on this data, the precise actions of the attitude adjustment trolleys are controlled to ensure that the main section moves along the preset trajectory. The main section and its accompanying attitude adjustment trolleys are considered as an integrated six-degree-of-freedom automatic alignment parallel system, where the main section acts as the moving platform, and each attitude adjustment trolley provides the system's power support. By performing inverse kinematics analysis of the system, the dynamic trajectory parameters that the attitude adjustment trolleys must follow in different directions can be solved.

[0160] Step 2.1: Measure the position of the center of the rotating ball head of the attitude adjustment trolley, and convert the measurement data to the coordinate system of the moving section. The positions of the center of the rotating ball head of each trolley in the coordinate system of the moving section are as follows: , where n represents the number of attitude adjustment vehicles;

[0161] During the rotation of the main segment, the inverse kinematics of the attitude adjustment trolley is solved by the rotation matrix; during the translation of the main segment, only the simultaneous movement of four attitude adjustment trolleys is needed to achieve the translation of the main segment, so the trajectory of each trolley is consistent with the above-mentioned translation trajectory of the main segment.

[0162] The rotational adjustment of the main section takes time t1, and the translational adjustment of the main section takes time t2. Therefore, during the overall adjustment process of the ship's moving main section, the relative displacement of the adjustment trolley in the three degrees of freedom is:

[0163]

[0164] In the formula, R(t) is:

[0165]

[0166]

[0167]

[0168]

[0169] And in the formula, Taking the derivative of the above equation as a function of angle and time, we can obtain the expression for the velocity motion of each degree of freedom during the adjustment process of the overall segment rotation:

[0170]

[0171] Differentiating the above equation, we obtain the expression for the acceleration motion of each degree of freedom of the entire segment during the attitude adjustment process:

[0172]

[0173] Differentiating the above equation, we obtain the expression for the acceleration motion of each degree of freedom of the entire segment during the attitude adjustment process:

[0174]

[0175] Step 2.2: Constrain the velocity and acceleration of each attitude adjustment trolley. The constraint conditions are as follows:

[0176]

[0177] During the rotation of the entire section, the maximum velocity of each degree of freedom of the attitude adjustment trolley is limited to 10 mm / s, and the acceleration is limited to 2 mm. 2 / s; During the overall translation process, the maximum velocity of each degree of freedom of the attitude adjustment trolley is limited to 30mm / s, and the acceleration is limited to 2mm. 2 / s.

[0178] Step 3 specifically involves:

[0179] Solving the time-optimal trajectory of the attitude adjustment trolley under velocity and acceleration constraints using the bisection method only considers time. However, in actual ship section alignment, many trolleys need to be linked and their attitude adjusted, resulting in high energy consumption and cost. Therefore, optimizing energy consumption is particularly important. Secondly, if the impact of the attitude adjustment trolley is too large, it will cause slight deformation of the ship's bottom plane and increase the vibration of the trolley during movement, thereby shortening the service life of the attitude adjustment trolley and causing larger alignment errors. Therefore, the effects of energy consumption and impact should also be taken into account in actual practice. Thus, a multi-objective optimization of the attitude adjustment trolley trajectory is performed. The specific process is as follows: Figure 1 As shown.

[0180] First, based on the determined alignment method and trajectory planning method of the overall segment, and combined with the constraints, a multi-objective function of time-energy consumption-impact degree is established. Then, the improved whale algorithm is used to solve the multi-objective optimization model, thereby realizing the multi-objective trajectory optimization of the overall segment and the attitude adjustment vehicle.

[0181] Step 3.1: Establish the objective function for trajectory optimization.

[0182] To address the issues of high energy consumption and significant impact during attitude adjustment in large ship section automatic alignment systems, multi-objective programming is implemented for each trolley during the overall attitude adjustment process of the section, and the objective function is defined as follows:

[0183]

[0184] In the formula, st is the total number of pose adjustment steps, st=2; t i This represents the time taken in step i; T is the running time of the attitude adjustment trolley, and N represents the number of trolleys, N=4; , f1 represents the total acceleration and total jerk of the nth attitude adjustment vehicle in the three degrees of freedom during step i; f2 represents the motion time of the entire attitude adjustment process; f3 represents the energy consumption index of all attitude adjustment vehicles during the attitude adjustment process; f4 represents the joint impact index of all attitude adjustment vehicles.

[0185] Step 3.2: Solving the integral based on Simpson's method

[0186] Solving Simpson's integrals by dividing the integration interval [a, b] into many intervals, i.e., the composite Simpson's integral method, involves dividing the integration interval [a, b] into 2n equal-width subintervals [x, b, ..., x]. k x k +1], the length of each interval is Let 2n be the number of subintervals, and n be a positive integer. Then the corresponding composite Simpson integral formula is as follows:

[0187]

[0188] In the formula, a=0; b=t1, representing the completion time of the first stage of the overall segment;

[0189] The error formula is:

[0190]

[0191] In the formula, f (4) It is the maximum value of the fourth derivative of f(x) in the interval [a, b], where This plan f (4) There is no solution set near 0, therefore f (4) Approximately identified as The maximum value of the fourth derivative in the interval [1, b], with the subinterval n=400.

[0192] Step 3 specifically involves:

[0193] (1) Whale optimization algorithm

[0194] The Whale Optimization Algorithm is an intelligent algorithm that mimics the foraging behavior of whales. This algorithm has advantages such as few parameters and fast convergence speed. The main process of the algorithm is as follows:

[0195] In the whale optimization algorithm, when searching for prey, the whale group first determines the location of the prey and updates its own position based on the current optimal position. Based on the exploration behavior in round t, when |A| is greater than 1, the whales will adjust their exploration behavior in round t+1. The specific process is described below:

[0196]

[0197] In the formula: t represents the distance between the whale and its food; t represents the current iteration number; A and c are coefficient vectors. This is the best location for whales; This is the current position of the whale. The coefficient vectors A and c can be represented by equations (4.33) and (4.34).

[0198]

[0199]

[0200] In the formula: r represents a random number between 0 and 1. t represents the current iteration round, while Tmax is the maximum set iteration round. The parameter a gradually decreases linearly from 2 to 0, and the parameter A also decreases accordingly as a decreases. When the parameter |A| decreases to 1 or below, the optimization algorithm transitions from the prey-finding stage to the prey-hunting stage.

[0201] As the iteration process continues, when the value of |A| decreases to 1 or below, the algorithm transitions to the prey-encircling phase. At this point, the remaining whales update their positions based on the currently known optimal location information, gradually narrowing the encirclement to approach the prey and ultimately determining the target location for capture.

[0202]

[0203] In the formula, Let x*(t) be the optimal solution for each iteration. When A∈ When the random value is between, Iterative updates from x(t) to x*(t) gradually approach the optimal solution.

[0204] Whales employ a unique hunting technique: expelling bubbles while swimming upwards in a spiral motion. This allows them to gradually surround and push their prey towards the surface, maximizing the chances of a successful capture. This distinctive bubble-based attack can be described using the following mathematical model:

[0205]

[0206] In the formula: b is the constant coefficient of the spiral equation, and in this study, b=1 is taken. This indicates the distance to the optimal whale. l is a random number in the interval [-1, 1].

[0207] To simulate the simultaneous execution of encirclement and bubble-hunting strategies by whales, a random probability was used to determine their position update strategy. This means that the probability of selecting both encirclement and bubble-hunting methods is set to 50%. Based on this, the whale's position update can be calculated and represented by the following formula:

[0208]

[0209] Step 3.3: Solve the multi-objective optimization model using the improved whale algorithm to achieve multi-objective trajectory optimization for the total segment and the attitude adjustment vehicle. Specifically:

[0210] An improved whale optimization algorithm was obtained by improving the population initialization, weights, convergence factor, and search capability in the whale optimization algorithm.

[0211] The initial population layout of an algorithm directly affects its ability to search for the optimal solution and its fast convergence performance. Among these, a balanced initial population is particularly crucial for improving the overall efficiency of the algorithm. In traditional applications, the Whale Optimization Algorithm (WOA) uses randomization to achieve the initial population configuration, which may lead to an imbalance in population distribution.

[0212] The initialization of the population in the whale optimization algorithm is improved by using a Hammersley low-discrepancy sequence to optimize the initial distribution of the population, thus promoting the uniformity of the population distribution. However, individuals in the randomly distributed initial population have a probability of appearing near the optimal value. Therefore, a judgment mechanism is added: if the initially randomly distributed population produces better values ​​in the first solution, then the randomly distributed population is used as the initial value. To demonstrate the spatial distribution difference between random distribution and random numbers generated using a Hammersley sequence, a population of 100 individuals is generated in the interval [0, 1], and the graphical comparison of the two distribution methods is shown below. Figure 2 The population distribution generated using the Hammersley sequence exhibits higher uniformity and more comprehensive coverage of the solution space. The formula for generating the initial population using the Hammersley sequence is shown below:

[0213]

[0214] In the formula: x i The initial position of the individual; X lb This represents the lower limit of an individual variable; X up The upper limit of the individual variable; H is a random number in the [0, 1] range generated by Hammersley;

[0215] The weights of the population in the whale optimization algorithm are improved by introducing the weight concept from the particle swarm optimization algorithm into the whale algorithm. In order to address the problem that the weights are generally linear functions and have poor convergence, an adaptive weight strategy is proposed.

[0216]

[0217] The adaptive weights proposed in this invention exhibit a non-linear decreasing trend as iterations increase. Larger weights in the early stages are beneficial for the algorithm to escape local optima. The position update formula for the whale algorithm after adding weights is as follows:

[0218]

[0219]

[0220]

[0221] In the improved Whale Optimization (WOA) algorithm, adjusting the parameter A significantly impacts the balance between the exploration and exploitation phases, primarily controlled by the convergence factor 'a'. By default, the parameter 'a' decreases linearly with each iteration. This decrease may lead to insufficient exploration in the early stages and slow aggregation near the end. To ensure the algorithm prioritizes global search in the early iterations and local search in the later stages, the decrease in 'a' is changed to a non-linear decrease. The non-linear convergence factor update formula is as follows:

[0222]

[0223] To improve the search capability of the population in the whale optimization algorithm, the Levy flight trajectory mechanism helps to expand the population diversity of the algorithm, and can better balance the local search and global search capabilities. In IWOA, c is replaced with the isotropic Levy step size, and the process is as follows:

[0224]

[0225]

[0226]

[0227] In the formula, Levy is the step size extracted from the Levy distribution, and Γ(λ) is the standard gamma function. U and V follow normal distributions with a mean of zero, and σ 2 u and σ 2 v Let Variance be the variance.

[0228] Step 3 specifically involves:

[0229] Step 3.4: Solving the objective function based on IWOA

[0230] Before using the IWOA algorithm to solve the time-energy-impact function, the objective function is normalized to eliminate dimensions. The normalization formula is as follows:

[0231]

[0232] In the formula: f inew f is the new dimensionless function after normalization of the i-th objective function; i (x) min f is the minimum function value of the i-th objective function within the range; i (x) max Let be the maximum function value of the i-th objective function within the range;

[0233] This study defines the total rotation and attitude adjustment time range as [0, 150], and the translation time as [0, 150]. The maximum and minimum values ​​of each objective function within the above interval (from the optimal time to the maximum defined time) are the required values ​​for the above functions.

[0234] To better determine the weight of each objective in the optimization process, the normalized objective function is weighted, and the constructed normalized weighted objective function is as follows:

[0235]

[0236] In the formula, , , The weighting coefficients define the importance of each objective in the alignment of the ship sections. Different projects have different focuses and therefore assign different weights. This study aims to find the most balanced values ​​and assigns them according to an equal weighting method. ;

[0237] The optimal time for the overall segment rotation and translation process is usually solved using the bisection method. This invention uses the optimal time satisfying the constraints, obtained by the bisection method, as the minimum time f1(x) within the objective function's f1 interval. min The maximum time limit is defined as f1(x). max The above objective function is f2(x). min f2(x) max f3(x) min f3(x) max Numerical solutions can be obtained by using the maximum and minimum time parameters of the trajectory, thereby solving the normalized objective function.

[0238] The concept of normalized weights can transform multiple objectives into a single objective, but this single objective is still a relatively complex function. Conventional solution methods are time-consuming and computationally intensive. Intelligent algorithms can solve the objective function faster and more accurately. Therefore, this invention combines the above-mentioned improved whale algorithm optimization algorithm to solve the final objective function.

[0239] Before using the IWOA algorithm to solve the time-energy-impact function, during multi-objective optimization, it is necessary to consider constraints such as trajectory velocity and acceleration. Therefore, during the IWOA update iteration process, cases that do not meet the constraints need to be excluded. An external penalty factor is added to the objective function to increase the fitness of parameters outside the constraint range. When searching for the minimum of the objective function, the process of updating the population optimum is skipped. The objective function after adding the penalty factor is as follows:

[0240]

[0241] In the formula, f(x) represents an unconstrained initial function; K is the penalty coefficient, which is set to K=1000 in this study; Let g(x) be the maximum number of iterations; g(x) be the constraint condition. When the constraint condition is met, g(x) = 0; when the constraint condition is not met, g(x) = 1. By solving the above objective function and finding the two time intervals that minimize F(x) within the constraint range, the obtained time intervals are the optimal solutions under the multi-objective equilibrium condition.

[0242] Step 4 specifically involves:

[0243] Under the above-mentioned speed and acceleration constraints, the attitude adjustment of the whole segment is planned. During the rotation and translation of the whole segment, the bisection method is used to solve for the optimal time within the constraints.

[0244] Using a seventh-order polynomial trajectory fitting method and applying the bisection method, the solution time is as follows:

[0245]

[0246] In the formula This refers to the total alignment time of the segment;

[0247] Considering practical engineering conditions, the movement speed and working stroke of the three-dimensional adjustable trolley must meet certain constraints:

[0248]

[0249] In the formula, This indicates the maximum speed of the three-dimensional adjustable vehicle. , , These represent the maximum working stroke of the three-dimensional adjustable trolley in the x, y, and z directions, respectively; i = 1, 2, 3, 4 represent each adjustable trolley.

[0250] Combining the kinematic equations summarized above, by selecting an appropriate total segment alignment time for the above equation, we can obtain the motion trajectories of each three-dimensional adjustable vehicle in each direction that satisfy the constraints. Considering that in engineering practice we generally require the total segment alignment time to be as small as possible, we adopt the minimum total segment alignment time as the objective of motion trajectory planning. The mathematical model is as follows:

[0251] Target constraint

[0252]

[0253] The optimization problem described above is solved using the bisection method, with the specific steps as follows:

[0254] Step (1): Based on the initial pose, target pose, and maximum speed requirements of the three-dimensional adjustable trolley in each direction of the hull section, a preliminary range of the alignment time [t1, t2] is given, and t is obtained. f =t1,t f The equation of the motion trajectory of the total segment pose at time t2 is:

[0255]

[0256]

[0257] Step (2): Based on the trajectory equation and kinematic equation of the overall pose above, calculate t respectively. f =t1,t f At time t2, the maximum speed of each three-dimensional adjustable trolley in the x, y, and z directions;

[0258] It should be noted that directly calculating the motion speed of each 3D adjustable vehicle in each direction using analytical methods is extremely complex. A simpler approach is to discretize the total alignment time, with the discretization time interval being as small as possible. Generally, it can be taken to be the same as the sampling period of the actual control system, that is, to approximate the motion speed of the 3D adjustable vehicle in each direction changes linearly within one sampling period. Then, the motion speed of the 3D adjustable vehicle in each direction at each time point can be calculated, thereby obtaining the maximum motion speed of the 3D adjustable vehicle in each direction at the current total alignment time.

[0259] Step (3), if t f =t1,t f =t2 does not satisfy the constraint condition, which means that the values ​​of t1 and t2 are incorrect. At this time, we should go back to step (1) to reset the range of the total segment docking time.

[0260] Step (4), if t f =t1,t f =f2 does not satisfy the constraint condition, then the optimal total segment alignment time t opt =t1, calculation ends;

[0261] Step (5), if t f =t1 does not satisfy the constraint condition, while t f =t2 satisfies the constraint conditions, then let ;

[0262] Step (6), if t f If t3 satisfies the constraint condition, then let t2 = t3; otherwise, let t1 = t3. Repeat step 5 until t2 - t1 ≤ δ. opt =t1 is the optimal total segment alignment time;

[0263] Step (7): Substitute someone to obtain t f =t opt Equation of the total segment docking trajectory at time:

[0264]

[0265] By combining the kinematic equations, the displacement, velocity, and acceleration of the ball center of each three-dimensional adjustable trolley process joint in the X, Y, and Z directions at each moment can be obtained. The data is then output and saved to complete the calculation.

[0266] Step 5 specifically involves:

[0267] Boolean constraints and kinematic pair constraints are added to the established model. Boolean constraints combine multiple parts of the orientation adjustment vehicle into fewer parts, facilitating kinematic simulation. Simultaneously, kinematic pair constraints define the motion directions of the parts within the orientation adjustment vehicle. Then, a kinematic simulation of the overall segment alignment is performed, and the accuracy of the trajectory planning is assessed based on the simulation results.

[0268] Step 5.1 Set kinematic pair constraints

[0269] ① Fixed pair constraint

[0270] The components that do not participate in movement are fixedly connected to the ground via fixed joints. These non-moving components include four support piers, a fixed section, and four tracks. The ball joint of the attitude adjustment trolley should be fixed as a separate part, rather than being linked to the telescopic rod of the lifting mechanism via Boolean operations. This is because it makes it easier to find the coordinates of the ball joint's center during subsequent constraint processes. Therefore, the lifting mechanism and the trolley ball joint are fixed together using fixed joint constraints.

[0271] ②Moving joint constraint

[0272] To simplify the mechanism's motion, the movement of the bottom hub guide rail of the attitude adjustment trolley is approximated as planar motion, and a sliding joint is added to allow the bottom platform to slide on the track. Similarly, a sliding joint is set between the middle platform and the bottom platform of the attitude adjustment trolley to simplify the motion of the ball screw of the middle platform. The lifting motion of the attitude adjustment trolley can be directly regarded as a cylindrical joint.

[0273] ③ Spherical pair constraint

[0274] During attitude adjustment, the ship section needs to rotate around the ball joint on the top of the attitude adjustment trolley. Therefore, a ball joint needs to be added to the ball joint structure of the attitude adjustment trolley to give the ball joint and the ball joint base a passive rotation constraint.

[0275] Step 5.2: Perform overall segment alignment kinematic simulation.

[0276] (1) Driver settings

[0277] Add drives to the aforementioned prismatic joints that require active movement. The XYZ drive direction of the attitude adjustment trolley must be consistent with the XYZ direction of the designated global coordinate system. The ball joints are not driven and are treated as passive mechanisms. Add drives to the prismatic joints in the XYZ direction on the trolley. The drive curves mentioned above are the displacement curves exported after software calculation. Import the trolley curves by selecting "Experimental Data" and establish the drive curves for each trolley using the CUBSPL function.

[0278] (2) Overall alignment kinematic simulation analysis

[0279] After establishing each drive mechanism, a set of 35 points corresponding to the fixed and moving segments is created, and the Euclidean distance between corresponding points is measured using a position measurement function. The total time is set to 178.21 seconds, and kinematic simulation is performed based on the theoretical pose data from the pose calculation section. The initial state is as follows: Figure 3 As shown, the rotation is completed as follows Figure 4 As shown, the overall alignment is complete. Figure 5 As shown.

[0280] Through the above simulation analysis, it is clear that after the rotational attitude adjustment, the angular deviation of the entire segment has been adjusted, and after the translational adjustment, the alignment surface has been aligned. Measurements were taken at 35 key measurement points on the alignment surface of the entire segment, such as... Figure 6 As shown, the Euclidean distance error of each key measurement point was measured simultaneously. The Euclidean distance error curve is obtained as follows: Figure 7 As shown.

[0281] pass Figure 6 It can be seen that, as time increases, the distance difference between the 35 pairs of key measurement points approaches 0, and the final error value decreases from... Figure 7 It can be seen that the errors of the 35 key measurement points are all very small, with error values ​​within 0.012mm, which indicates the feasibility and accuracy of trajectory planning and meets the alignment requirements of the overall section in the project.

[0282] Step 6: Conduct multi-objective optimization experiments and overall alignment experiments for the entire segment to verify the feasibility of multi-objective optimization of the segment trajectory and the accuracy of the overall alignment trajectory planning.

[0283] Step 6.1: Multi-objective optimization experiment verification of the overall segment

[0284] First, an experimental platform was built using sensor equipment. A speed measurement sensor was installed on each attitude adjustment vehicle. By measuring the speed, energy consumption and impact intensity were calculated. The sensors were distributed as follows: Figure 8 As shown in the figure. The sensor distribution on a single attitude adjustment vehicle is as follows. Figure 8 As shown in the left-middle diagram, the sensor on the left measures the acceleration of the alignment trolley, while the sensor on the right indirectly measures the velocity of the alignment trolley using an integration method. Both sensors utilize the RS485 communication protocol. The overall sensor distribution of the alignment system is as follows: Figure 8 As shown in the middle right figure, by measuring the speed and acceleration of each attitude adjustment vehicle and substituting them into the multi-objective objective function, the relevant energy consumption index and impact index are calculated.

[0285] While ensuring the alignment method and trajectory planning placement are identical, an optimization method aiming for optimal time is used as a control group. Ten sets of experiments are conducted, and the energy consumption and impact index values ​​are recorded for each set of experiments. Energy consumption indexes are as follows: Figure 9 As shown in the middle left figure, the impact index is as follows: Figure 9 As shown in the middle right figure.

[0286] It can be seen that both energy consumption and impact performance indicators have decreased. Furthermore, after calculation, the average value of the original energy consumption index experimental data was 9.65, while the average value of the optimized energy consumption index was 2.35. The average value of the original impact index experimental data was 2.01, while the average value of the optimized impact index was 0.18. This indicates that the energy consumption and impact of the optimized trajectory have decreased to varying degrees, proving the correctness of the multi-objective optimization of the trajectory in this chapter.

[0287] Step 6.2: Overall alignment test verification of the entire segment

[0288] Based on the above-mentioned total segment data measurement and pose calculation experiments, the trajectory planning content of this study was applied to the total segment pose adjustment experiment to verify the alignment of the total segment. After the pose adjustment was completed, the alignment of the total segment was as follows: Figure 10 As shown.

[0289] As shown in the figure above, the alignment of the entire section's end faces has been achieved. Using two total stations, measurements were taken at the relative points on the outer side of the entire section. The errors in the XYZ directions of the 35 pairs of points on the alignment surface were calculated based on the relative relationships. Figure 11 As shown in the middle left figure. The Euclidean distance error is as follows: Figure 11 As shown in the middle right figure.

[0290] The above experiments show that the error of the key measurement points on the alignment surface in the XYZ direction is within ±2mm, and the Euclidean distance error is within 2.5mm, which meets the technical requirements for precise alignment of the entire section.

[0291] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0292] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-target trajectory optimization method based on IWOA (Integrated WOA) for total segment alignment, characterized in that, Includes the following steps: Step 1: Select the alignment method based on the completed attitude adjustment trolley position and attitude calculation results, and adjust the position and attitude of the ship section through the coordinated operation of the attitude adjustment trolley; and determine the trajectory planning method of the ship section according to the given task requirements. Step 2: View the main section and its supporting attitude adjustment trolley as an automatic alignment parallel system integrating six degrees of freedom. The main section serves as the mobile platform, while multiple attitude adjustment trolleys constitute the power support of the system. By performing inverse kinematics analysis on the system, the dynamic trajectory parameters that the attitude adjustment trolleys need to follow in different directions are obtained. Step 3: Based on the determined overall alignment method and trajectory planning method, and combined with the speed and acceleration constraints of the attitude adjustment vehicle, establish a multi-objective function of time-energy consumption-impact degree, and further solve the multi-objective optimization model through the improved whale algorithm to achieve multi-objective trajectory optimization of the overall segment and the attitude adjustment vehicle. Step 4: Simulate and analyze the multi-objective optimization process. Similarly, based on the posture calculation results of the attitude adjustment vehicle in Step 1, and combined with the speed and acceleration constraints of the attitude adjustment vehicle, plan the attitude adjustment of the whole segment. During the rotation and translation process of the whole segment, the bisection method is used to solve the optimal time within the constraint range. Based on the above multi-objective function, the improved whale algorithm is used to solve the objective function, thereby calculating the total rotation and translation process time. The motion trajectory of the attitude adjustment vehicle is solved by time parameters, seventh-order polynomial trajectory planning method, and speed and acceleration constraints of the attitude adjustment vehicle. Step 5: While ensuring that the basic motion mode and motion constraints of the attitude adjustment vehicle are consistent, simplify the design model of the attitude adjustment vehicle and use ADAMS software to establish the overall alignment model of the attitude adjustment vehicle without an internal transmission system. Boolean constraints and kinematic pair constraints are added to the established model. Boolean constraints combine multiple parts of the orientation adjustment vehicle into fewer parts, facilitating kinematic simulation. Simultaneously, kinematic pair constraints define the motion directions of the parts within the orientation adjustment vehicle. Then, a kinematic simulation of the overall segment alignment is performed, and the accuracy of the trajectory planning is assessed based on the simulation results. Step 6: Conduct multi-objective optimization experiments and overall alignment experiments for the entire segment to verify the feasibility of multi-objective optimization of the segment trajectory and the accuracy of the overall alignment trajectory planning.

2. The multi-target trajectory optimization method based on IWOA segment alignment according to claim 1, characterized in that, Step 1 specifically involves: A two-step alignment method is adopted as the overall segment posture adjustment alignment method. The two-step alignment method is as follows: First, the roll, pitch, and yaw angles of the ship section are adjusted to achieve angular alignment. Then, fine position adjustments are made in the three main axis directions X, Y, and Z to complete the entire alignment operation. The trajectory of the ship's total section is planned using a seventh-order polynomial. The expression for the seventh-order polynomial planning is as follows: ； Let the initial time be t0=0 and the final time be t f Its constraints are: ； Substituting the constraints into the above equation, the values ​​of each parameter can be solved: ； make The trajectory of α can be obtained: ； Similarly, the trajectories of the total segments x, y, z, β, and γ can be obtained: 。 3. The multi-target trajectory optimization method based on IWOA segment alignment according to claim 1, characterized in that, Step 2 specifically involves: Step 2.1: Measure the position of the center of the rotating ball head of the attitude adjustment trolley, and convert the measurement data to the coordinate system of the moving section. The positions of the center of the rotating ball head of each trolley in the coordinate system of the moving section are as follows: , where n represents the number of attitude adjustment vehicles; During the rotation of the main segment, the inverse kinematics of the attitude adjustment trolley is solved by the rotation matrix; during the translation of the main segment, only the simultaneous movement of four attitude adjustment trolleys is needed to achieve the translation of the main segment, so the trajectory of each trolley is consistent with the above-mentioned translation trajectory of the main segment. The rotational adjustment of the main section takes time t1, and the translational adjustment of the main section takes time t2. Therefore, during the overall adjustment process of the ship's moving main section, the relative displacement of the adjustment trolley in the three degrees of freedom is: ； In the formula, R(t) is: ； ； ； ； And in the formula, Taking the derivative of the above equation as a function of angle and time, we can obtain the expression for the velocity motion of each degree of freedom during the adjustment process of the overall segment rotation: ； Differentiating the above equation, we obtain the expression for the acceleration motion of each degree of freedom of the entire segment during the attitude adjustment process: ； Differentiating the above equation, we obtain the expression for the acceleration motion of each degree of freedom of the entire segment during the attitude adjustment process: 。 4. The multi-target trajectory optimization method based on IWOA segment alignment according to claim 3, characterized in that, Step 2 specifically involves: Step 2.2: Constrain the velocity and acceleration of each attitude adjustment trolley. The constraint conditions are as follows: ； During the rotation of the entire section, the maximum velocity of each degree of freedom of the attitude adjustment trolley is limited to 10 mm / s, and the acceleration is limited to 2 mm / s². 2 During the overall translation process, the maximum velocity of the attitude adjustment trolley in each degree of freedom is limited to 30 mm / s, and the acceleration is limited to 2 mm / s². 2 .

5. The multi-target trajectory optimization method based on IWOA segment alignment according to claim 1, characterized in that, Step 3 specifically involves: Step 3.1: Establish the objective function for trajectory optimization. To address the issues of high energy consumption and significant impact during attitude adjustment in large ship section automatic alignment systems, multi-objective programming is implemented for each trolley during the overall attitude adjustment process of the section, and the objective function is defined as follows: ； In the formula, st is the total number of pose adjustment steps, st=2; t i This represents the time taken in step i; T represents the running time of the attitude adjustment trolley, and N represents the number of trolleys, N=4; , f1 represents the total acceleration and total jerk of the nth attitude adjustment vehicle in the three degrees of freedom during step i; f2 represents the motion time of the entire attitude adjustment process; f3 represents the energy consumption index of all attitude adjustment vehicles during the attitude adjustment process; f4 represents the joint impact index of all attitude adjustment vehicles. Step 3.2: Solving the integral based on Simpson's method Solving Simpson's integrals by dividing the integration interval [a, b] into many intervals, i.e., the composite Simpson's integral method, involves dividing the integration interval [a, b] into 2n equal-width subintervals [x, b, ..., x]. k x k +1], the length of each interval is Let 2n be the number of subintervals, and n be a positive integer. Then the corresponding composite Simpson integral formula is as follows: ； In the formula, a=0; b=t1, representing the completion time of the first stage of the overall segment; The error formula is: ； In the formula, f (4) It is the maximum value of the fourth derivative of f(x) in the interval [a, b], where .

6. The multi-target trajectory optimization method based on IWOA segment alignment according to claim 1, characterized in that, Step 3 specifically involves: Step 3.3: Solve the multi-objective optimization model using the improved whale algorithm to achieve multi-objective trajectory optimization for the total segment and the attitude adjustment vehicle. Specifically: An improved whale optimization algorithm was obtained by improving the population initialization, weights, convergence factor, and search capability in the whale optimization algorithm. The initialization of the population in the improved whale optimization algorithm is optimized by using Hammersley low-discrepancy sequences to improve the initial distribution of the population and promote its uniformity. The formula for using the Hammersley sequences to generate the initial population is shown below: ； In the formula: x i The initial position of the individual; X lb This represents the lower limit of an individual variable; X ub is the upper limit of the individual variable; H is a random number in the [0, 1] range generated by Hammersley; The weights of the population in the whale optimization algorithm are improved by introducing the weight concept from the particle swarm optimization algorithm into the whale algorithm. In order to address the problem that the weights are generally linear functions and have poor convergence, an adaptive weight strategy is proposed. ； After adding weights, the position update formula for the whale algorithm is: ； ； ； The convergence factor of the population in the improved whale optimization algorithm is changed from a non-linear decrease to a non-linear decrease. The update formula for the non-linear convergence factor is: ； To improve the population search capability of the whale optimization algorithm, in IWOA, c is replaced with the isotropic Lévy step size, and the process is as follows: ； ； ； In the formula, Levy is the step size extracted from the Levy distribution, Γ(λ) is the standard gamma function, U and V follow normal distributions with a mean of zero, and σ 2 u and σ 2 v Let Variance be the variance.

7. The multi-target trajectory optimization method based on IWOA segment alignment according to claim 6, characterized in that, Step 3 specifically involves: Step 3.4: Solving the objective function based on IWOA Before using the IWOA algorithm to solve the time-energy-impact function, the objective function is normalized to eliminate dimensions. The normalization formula is as follows: ； In the formula: f inew f is the new dimensionless function after normalization of the i-th objective function; i (x) min f is the minimum function value of the i-th objective function within the range; i (x) max Let be the maximum function value of the i-th objective function within the range; To better determine the weight of each objective in the optimization process, the normalized objective function is weighted, and the constructed normalized weighted objective function is as follows: ； In the formula, , , The weighting coefficients define the importance of each objective in the alignment of the ship sections. Different projects have different focuses and therefore assign different weights. This study aims to find the most balanced values ​​and assigns them according to an equal weighting method. ; By adding an external penalty factor to the objective function, the fitness of parameters outside the constraints is increased. When searching for the minimum of the objective function, the process of updating the population optimum is skipped. The objective function after adding the penalty factor is: ； In the formula, f(x) represents an unconstrained initial function; K is the penalty coefficient, which is set to K=1000 in this study; Let g(x) be the maximum number of iterations; g(x) be the constraint condition. When the constraint condition is met, g(x) = 0; when the constraint condition is not met, g(x) = 1. By solving the above objective function and finding the two time intervals that minimize F(x) within the constraint range, the obtained time intervals are the optimal solutions under the multi-objective equilibrium condition.

8. The multi-target trajectory optimization method based on IWOA segment alignment according to claim 1, characterized in that, Step 4 specifically involves: Under the above-mentioned speed and acceleration constraints, the attitude adjustment of the whole segment is planned. During the rotation and translation of the whole segment, the bisection method is used to solve for the optimal time within the constraints. Using a seventh-order polynomial trajectory fitting method and applying the bisection method, the solution time is as follows: ； In the formula This refers to the total alignment time of the segment; Considering practical engineering conditions, the movement speed and working stroke of the three-dimensional adjustable trolley must meet certain constraints: ； Combining the kinematic equations summarized above, by selecting an appropriate total segment alignment time for the above equation, we can obtain the motion trajectories of each three-dimensional adjustable vehicle in each direction that satisfy the constraints. Considering that in engineering practice we generally require the total segment alignment time to be as small as possible, we adopt the minimum total segment alignment time as the objective of motion trajectory planning. The mathematical model is as follows: Target constraint ； The optimization problem described above is solved using the bisection method, with the specific steps as follows: Step (1): Based on the initial pose, target pose, and maximum speed requirements of the three-dimensional adjustable trolley in each direction of the hull section, a preliminary range of the alignment time [t1, t2] is given, and t is obtained. f =t1,t f The equation of the total pose at time t2 is: ； ； Step (2): Based on the trajectory equation and kinematic equation of the overall pose above, calculate t respectively. f =t1,t f At time t2, the maximum speed of each three-dimensional adjustable trolley in the x, y, and z directions; Step (3), if t f =t1,t f =t2 does not satisfy the constraint condition, which means that the values ​​of t1 and t2 are incorrect. At this time, we should go back to step (1) to reset the range of the total segment docking time. Step (4), if t f =t1,t f =f2 does not satisfy the constraint condition, then the optimal total segment alignment time t opt =t1, calculation ends; Step (5), if t f =t1 does not satisfy the constraint condition, while t f =t2 satisfies the constraint conditions, then let ; Step (6), if t f If t3 satisfies the constraint condition, then let t2 = t3; otherwise, let t1 = t3. Repeat step 5 until t2 - t1 ≤ δ. opt =t1 is the optimal total segment alignment time; Step (7): Substitute someone to obtain t f =t opt Equation of the total segment docking trajectory at time: ； By combining the kinematic equations, the displacement, velocity, and acceleration of the ball center of each three-dimensional adjustable trolley process joint in the X, Y, and Z directions at each moment can be obtained. The data is then output and saved to complete the calculation.

Images